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math.NT2022
Weil Sums over Small Subgroups
Alina Ostafe, Igor E. Shparlinski, José Felipe Voloch
We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial.…
math.NT2022
Cyclotomic and abelian points in backward orbits of rational functions
Andrea Ferraguti, Alina Ostafe, Umberto Zannier
We prove several results on backward orbits of rational functions over number fields. First, we show that if is a number field, and then the extension of $…
math.NT2022★ 1 cited
Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices
Philipp Habegger, Alina Ostafe, Igor E. Shparlinski
We consider the set of -matrices with integer elements of size at most and obtain a new upper bound on the number of matrices from $\ma…